LMS in prominent system subspace for fast system identification

In many system identification applications, the unknown system is characterized by time-varying parameters. Therefore, fast on-line identification is required in order to keep the system stable and improve the control performance. In this paper, we show that the dimensionality of system identification can be dramatically reduced if the unknown system is sparse, in the sense that its parameter set has a concise representation when expressed in a proper basis. In such cases, the system identification can be effectively carried out in a subspace of reduced dimension. Based on this theory, we further proposed two new least-mean-square (LMS) algorithms, namely, prominent system subspace LMS (PSS-LMS) and enhanced PSS-LMS (PSS-LMS+) to exploit this sparsity for fast system identification. Finally, we conducted experiments to compare the convergence performances of PSS-LMS, PSS-LMS+, and conventional LMS using numerical simulation, and the results confirm the superior performances of the proposed algorithms.